Two policemen and two terrorists were killed here today in a shoot out between security forces and members of the leftist Turkist People's Liberation Army.

The leftist group, making a violent comeback after eight years underground, also shot and killed a businessman in Ankara today and, in phone calls to newspapers, claimed responsibility for slaying an American serviceman in Izmir yesterday.

The apparent revival of the Turkish People's Liberation Army injects another troubling element into Turkey's already turbulent scene.

The group, whose avowed aim is to overthrow the government and set up a proletarian state in Turkey, played little part in the violence, mainly between leftist and rightist youth, that last year claimed more than 800 lives.

Besides being beset with street violence, Turkey is undergoing its worst economic crisis in history and there is growing discontent with the governement's apparent failure to put things straight.

The clash here today occured when police, using armored vehicles, beseiged an apartment block at Beykoz, on the Bosporus, suspected of being a hideout for the leftist group.

When the occupants opened fire with automatic weapons, killing two policemen, security forces stormed the building. Two terrorists were shot dead in the attack. A third was wounded and another escaped.

The incidents came after a rash of bank and payroll robberies staged by the leftist group and the slaying of three night watchmen at police stations in Istanbul and Izmir in the past few days.

They occurred despite martial law in Istanbul, Ankara and 11 other Turkish provinces, declared by the government of Prime Minister Bulent Ecevit in December in an attempt to curb increasing political violence.

Apart from isolated incidents, the Turkish People's Liberation Army has been largely silent since 1972 when the Army captured and hanged three of its leaders after the organisation assassinated the Israeli consul in Istanbul and killed two British and one Canadian civilian technicians at a NATO radar station on the Black Sea coast.

The armed forces used the government's failure to cope with the violence as an excuse to order conservative prime minister. Suleiman Demirel out of office and launch a nationwide crackdown against the left.

Ecevit, meanwhile, said today that there is new hope of Turkey receiving fresh credits from the West to help it out of its economic difficulties.

He told reporters in Ankara that talks between Finance Minister Ziya Muezzinoglu and Internation Monetary Fund officials in Switzerland "will considerably speed up the mechanism for foreign aid to Turkey."

Muezzinoglu returned to Ankara Friday after talks in Zurich aimed at winning IMF approval of measures taken by the Ecevit government to put Turkey's ailing economy in order.

These measures include price increases up to 94 percent on petroleum products, construction materials, sugar and coal produced by the state, and a 5.7 percent currency devaluation against the U.S. dollar.

Although these measures fall somewhat short of IMF demands for sweeping steps to reduce the $2 billion annual deficit run up by state industries plus a hefy devaluation, it is believed the IMF will allow Turkey to resume drawing from its $450 million standby credit, which has been frozen for three months.

This could encourage Turkey's Western allies and private foreign banks to come through with promised loans to ease Turkey's chronic foreign exchange shortage.

These new loans, however, will probably fall far short of the $1.5 billion Turkey says it needs to get its economy going again.